Home
Class 12
MATHS
Let F(x)=[cosx -sinx 0 ...

Let `F(x)=`[cosx -sinx 0 sinx cosx 0 0 0 1]` . `Show that `F(x)\ F(y)=F(x+y)``

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA ENGLISH|Exercise All Questions|181 Videos

  • ALGEBRA OF VECTORS

    RD SHARMA ENGLISH|Exercise All Questions|325 Videos

Similar Questions

Explore conceptually related problems

If F(x)=[[cosx,-sinx,0],[sinx,cosx,0],[ 0, 0, 1]] , show that F(x) F(y) = F(x + y) .

Let f(x)={(1-cosx)/(x^2),\ \ \ w h e n\ x!=0 ; 1,\ \ \ \ w h e n\ x=0 . Show that f(x) is discontinuous at x=0 .

If f(x) = [(cos x , - sinx,0),(sinx,cosx,0),(0,0,1)] then show f(x) . f(y) = f(x+y)

Let f(x)=(1-cosx)/(x^2),\ \ \ w h e n\ x!=0,\ f(x)=1,\ \ \ w h e n\ x=0 . Show that f(x) is discontinuous at x=0 .

If f(x)=|cosx-sinx| , then f'(pi/4) is equal to

If f(x)=|cosx-sinx| , then f'(pi/2) is equal to

Show that the function f(x) given by f(x)={(sinx)/x+cosx ,\ \ x!=0 2,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=0 ,mmm m m is continuous at x=0 .

The function f(x) = (1-sinx + cosx)/(1+sinx+cosx) is not defined at x = pi . The value of f(pi) , so that f(x) is continuous at x = pi , is

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is

The function f(x)=sinx+cosx will be

RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. Prove that the product of matrices [cos^2thetacosthetasinthetacosthe...

    Text Solution

    |

  2. Let A=[(0,-tan(alpha/2)),(tan(alpha/2),0)] and I be the identity matr...

    Text Solution

    |

  3. Let F(x)=[cosx -sinx 0 sinx cosx 0 ...

    Text Solution

    |

  4. Let A=[2 3-1 2] and f(x)=x^2-4x+7 . Show that f(A)=O . Use this result...

    Text Solution

    |

  5. If A=[0 1 0 0] , prove that (a I+b A)^n=a^n\ I+n a^(n-1)\ b A where I ...

    Text Solution

    |

  6. Let A ,\ B be two matrices such that they commute. Show that for an...

    Text Solution

    |

  7. Let A ,\ B be two matrices such that they commute. Show that for an...

    Text Solution

    |

  8. If A is a square matrix such that A^2=A , show that (I+A)^3=7A+I .

    Text Solution

    |

  9. If A is a square matrix such that A^2=I , then find the simplified...

    Text Solution

    |

  10. If A=[3\ \ \ 5] , B=[7\ \ \ 3] , then find a non-zero matrix C such...

    Text Solution

    |

  11. Compute the indicated products: [a b-b a][a-bb a] (ii) [1-2 2 3][1 ...

    Text Solution

    |

  12. Show that A B!=B A in the following case: A=[5-1 6 7] and B=[2 1 3 ...

    Text Solution

    |

  13. Compute the products A B and B A whichever exists in each of the fol...

    Text Solution

    |

  14. Compute the products A B and B A whichever exists in each of the fol...

    Text Solution

    |

  15. Show that A B!=B A in each of the following cases: A=[[1, 3,-1],[2,-...

    Text Solution

    |

  16. Evaluate the following: ([(1,3),( -1,-4))]+[(3 ,-2 ),(-1 ,1)])[(1 ,3,5...

    Text Solution

    |

  17. If A=[[1, 0],[ 0, 1]] , B=[[1,0],[0,-1]] and C=[[0, 1],[ 1, 0]] , then...

    Text Solution

    |

  18. If A=[[2,-1],[ 3, 2]] and B=[[0, 4],[-1, 7]] , find 3A^2-2B+I .

    Text Solution

    |

  19. If A=[[4, 2],[-1, 1]] , prove that (A-2I)(A-3I)=O .

    Text Solution

    |

  20. If A=[(1,1),(0,1)] , show that A^2=[(1, 2),( 0, 1)] and A^3=[(1 ,3 ),(...

    Text Solution

    |